To assess the common assumption that phase offsets $(Ф_0)$, i.e. the phase of complex coil sensitivities, are temporally stable and to investigate the validity of this assumption at 7T for long measurements made with multi-channel coils and large head rotations.

Phase for each channel $Ф_{ch}$ consist of echo-time-independent phase offset $Ф_{0,ch}$, and a term describing local variations from the static magnetic field, ΔB₀:

$$\phi_{ch}(TE)=\phi_{0,ch}+2\pi\gamma TE \triangle B_{0}$$

In order to create accurate B₀ field-maps (for correction of EPI distortions) or optimally combine phase data from multi-channel coils (for SWI or QSM) one needs to remove $Ф_{0,ch}$ from the phase from each channel. Several dynamic distortion correction methods share a common assumption that $Ф_0$ is temporally stable^1–4. They have only been tested for moderate motion, using volume coils and up to 3T, where $Ф_0$ varies slowly in space. At 7T with multi-channel coils and shorter RF wavelengths $Ф_0$ differs for each coil element and is more inhomogeneous, which increases its vulnerability during long acquisitions or motion (changing the coil loading). Changes in $Ф_0$ also influence the quality of phase combination, reducing SNR, in methods using a reference scan for $Ф_0$ estimation^5–7. To address these concerns we examine the variations in $Ф_{0,ch}$ due to technical causes and motion and their influence on the accuracy of field-mapping and phase combination.

Measurements were carried out with a 7T Siemens scanner and a 32-channel head coil. Changes in $Ф_{0,ch}$ caused by scanner instabilities were measured in a phantom during four dual-echo EPI scans of 10 min each (TEs=[9.4,27.9]ms, TR=2s, 3.2x3.2x3.2mm³, bandwidth=1532Hz/pix). Changes in $Ф_{0,ch}$ due to motion were investigated for three volunteers who rotated their head slowly but continuously about the left-right axis during the acquisition of dual-echo EPI. For one volunteer, additional dual-echo GE scans (with higher SNR and resolution than EPI) were acquired at 8 head poses with no motion during acquisition (TEs=[2.5,5.0]ms, TR=400ms, 1.6x1.6x2mm³, bandwidth=540Hz/pix).

Field-maps were calculated for all acquisitions using the Hermitian inner product⁸. These were multiplied by the first TE and subtracted from separate-channel phase data yielding $Ф_{0,ch}$ for all channels. GE scans were additionally used for evaluation of phase combination quality when $Ф_{0,ch}$ were acquired at a different pose than a target image (i.e. when motion occurred between the reference and the target scan). For this purpose combined complex data $C_{comb}^{t,r}$ were calculated according to⁶:

$$C_{comb}^{t,r}=\sum_{ch}M_{ch}^te^{i(\phi_{ch}^t-\phi_{0,ch}^r)}$$

where t and r denote the target and reference pose respectively, ch is a channel index. When r≠t the $Ф_{0,ch}^r$ were extrapolated outside the brain to account for motion. The combined phase was obtained from $angle(C_{comb}^{t,r})$. Errors in the phase were mapped by taking the absolute value of the difference between phase reconstructed using $Ф_{0,ch}^r$ with r=t (optimal solution with no motion) and r≠t (non-optimal solution with motion). The quality Q of phase combination was quantified using⁶:

$$Q=\frac{abs(C_{comb}^{t,r})}{\sum_{ch}M_{ch}^t}$$ .

During a 40min long phantom experiment the $Ф_{0,ch}$ increased slowly but remained small: the weighted mean change in $Ф_{0,ch}$ (with separate magnitudes as weights) from the beginning to the end of the experiment was 0.061±0.017rad.

Figure 1 presents $Ф_{0,ch}$ changes in 4 representative channels from GE scans with head rotation up to 12.0°. The weighted mean change in $Ф_{0,ch}$ was up to 0.22±0.13rad for 12.0° rotation (Fig.1e, channel 16). Changes in $Ф_{0,ch}$ were low at all poses in the regions characterized by high signal (Fig.1d). Similar results, with the same range of motion (12.0°), were obtained for EPI measurements.

Figure 2 shows phase images combined using $Ф_0^r$ with r=t=6 or r=t=8 (Fig.2b) and r=1, t=6 or t=8 (Fig.2c). The difference between those two scenarios is presented in Fig.2d, where phase errors up to 0.3rad occurred in a dorsal slice for 6.3° rotation between reference and target scan (Fig.2d, Pose 6) and 0.6rad for 12° rotation (Fig.2d, Pose 8). Those errors can be translated into distortion correction errors of about 0.1 (for 6.3°) and 0.2 (for 12°) voxel for a sequence parameters typical for whole-brain fMRI at 7T (9,10) (Fig.2c, scale in voxels). The quality of phase matching was reduced by up to 2% for the largest head rotation (Fig.2e).

Long EPI measurement (40min) and large motions cause changes in separate-channel $Ф_{0,ch}$ (0.22±0.13rad for 12.0° rotation), which have little effect on the combined phase images. Negligible unwarping errors of about 0.2 voxel and reduction in phase matching quality by only 2% allow us to conclude that the assumption of $Ф_{0,ch}$ temporal stability holds and phase combination and dynamic distortion correction methods based on this assumption should work at 7T with separate channel-coils and substantial motion.